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Volumn , Issue , 2007, Pages 50-1-50-16

Approximation algorithms for some optimal 2D and 3D triangulations

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EID: 84959397517     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/9781420010749     Document Type: Chapter
Times cited : (5)

References (68)
  • 1
    • 0005493482 scopus 로고
    • On indecomposable polyhedra
    • Bagemihl, F., On indecomposable polyhedra, Am. Math. Mon., 55(7), 411, 1948.
    • (1948) Am. Math. Mon , vol.55 , Issue.7 , pp. 411
    • Bagemihl, F.1
  • 2
    • 0001914423 scopus 로고
    • Mesh generation and optimal triangulation
    • 2nd ed., Du, D.-Z. and Hwang, F. K., Eds., World Scientific, Singapore
    • Bern, M. and Eppstein, D., Mesh generation and optimal triangulation, in Computing in Euclidean Geometry, 2nd ed., Du, D.-Z. and Hwang, F. K., Eds., World Scientific, Singapore, 1995, p. 47.
    • (1995) Computing in Euclidean Geometry , pp. 47
    • Bern, M.1    Eppstein, D.2
  • 3
    • 0004239501 scopus 로고
    • Mathematical aspects of numerical grid generation
    • Castillo, J. E., Ed., Mathematical aspects of numerical grid generation, SIAM, 1991.
    • (1991) SIAM
    • Castillo, J.E.1
  • 4
    • 51249179364 scopus 로고
    • Triangulating a simple polygon in linear time
    • Chazelle, B., Triangulating a simple polygon in linear time, Disc. and Comput. Geom., 6, 485, 1991.
    • (1991) Disc. and Comput. Geom , vol.6 , pp. 485
    • Chazelle, B.1
  • 5
    • 0003568836 scopus 로고
    • A polynomial time algorithm for the minmax angle triangulation
    • Edelsbrunner, H., Tan, T. S., and Waupotitsch, R., A polynomial time algorithm for the minmax angle triangulation, SIAM J. Sci. Stat. Comp., 13, 994, 1992.
    • (1992) SIAM J. Sci. Stat. Comp , vol.13 , pp. 994
    • Edelsbrunner, H.1    Tan, T.S.2    Waupotitsch, R.3
  • 6
    • 84942487435 scopus 로고
    • A quadratic time algorithm for the minmax length triangulation
    • Edelsbrunner, H. and Tan, T. S., A quadratic time algorithm for the minmax length triangulation, Proc. of FOCS, 1991, p. 414.
    • (1991) Proc. of FOCS , pp. 414
    • Edelsbrunner, H.1    Tan, T.S.2
  • 7
    • 0001465710 scopus 로고
    • Voronoi diagrams and Delaunay triangulations
    • Hwang, F. K. and Du, D.-Z., Eds., World Scientific, Singapore
    • Fortune, S., Voronoi diagrams and Delaunay triangulations, in Computing in Euclidean Geometry, Hwang, F. K. and Du, D.-Z., Eds., World Scientific, Singapore, 1992.
    • (1992) Computing in Euclidean Geometry
    • Fortune, S.1
  • 8
    • 84976826673 scopus 로고
    • Voronoi diagrams—a survey of a fundamental geometric data structure
    • Aurenhammer, F., Voronoi diagrams—a survey of a fundamental geometric data structure, ACM Comput. Surv., 23, 345, 1991.
    • (1991) ACM Comput. Surv , vol.23 , pp. 345
    • Aurenhammer, F.1
  • 9
    • 0038534791 scopus 로고
    • Constrained Delaunay triangulations
    • Chew, L. P., Constrained Delaunay triangulations, Algorithmica, 4, 97, 1989.
    • (1989) Algorithmica , vol.4 , pp. 97
    • Chew, L.P.1
  • 10
    • 84976861822 scopus 로고
    • An optimal algorithm for constructing the Delaunay triangulation of a set of line segments
    • Wang, C. and Schubert, L., An optimal algorithm for constructing the Delaunay triangulation of a set of line segments, Proc. 3rd ACM Symp. on Comput. Geom., 1987, p. 223.
    • (1987) Proc. 3Rd ACM Symp. on Comput. Geom , pp. 223
    • Wang, C.1    Schubert, L.2
  • 11
    • 0032107935 scopus 로고    scopus 로고
    • Finding the constrained Delaunay triangulation and constrained voronoi diagram of a simple polygon in linear-time
    • Chin, F. and Wang, C. A., Finding the constrained Delaunay triangulation and constrained voronoi diagram of a simple polygon in linear-time, SIAM J. Comput., 28(2), 471, 1998.
    • (1998) SIAM J. Comput , vol.28 , Issue.2 , pp. 471
    • Chin, F.1    Wang, C.A.2
  • 12
    • 0043272288 scopus 로고
    • Fast algorithms for greedy triangulation
    • Levcopoulos, C. and Lingas, A., Fast algorithms for greedy triangulation. BIT, 32, 280, 1992.
    • (1992) BIT , vol.32 , pp. 280
    • Levcopoulos, C.1    Lingas, A.2
  • 13
    • 0001077595 scopus 로고
    • Automatische Interpolation von Isolinien bei willk ürlichen Stützpunkten
    • Düppe, R. D. and Gottschalk, H. J., Automatische Interpolation von Isolinien bei willk ürlichen Stützpunkten, Allgemeine Vermessungsnachrichten, 77, 423, 1970.
    • (1970) Allgemeine Vermessungsnachrichten , vol.77 , pp. 423
    • Düppe, R.D.1    Gottschalk, H.J.2
  • 15
    • 0003136657 scopus 로고
    • Computing a subgraph of the minimum weight triangulation
    • Keil, J. M., Computing a subgraph of the minimum weight triangulation, Comput. Geom.: Theor. Appl., 4, 13, 1994.
    • (1994) Comput. Geom.: Theor. Appl , vol.4 , pp. 13
    • Keil, J.M.1
  • 16
    • 0343736947 scopus 로고    scopus 로고
    • A new subgraph of minimum weight triangulations
    • Wang, C. A., Chin, F. Y. L., and Xu, Y., A new subgraph of minimum weight triangulations, J. Comb. Opt., 1(2), 115, 1997.
    • (1997) J. Comb. Opt , vol.1 , Issue.2 , pp. 115
    • Wang, C.A.1    Chin, F.Y.L.2    Xu, Y.3
  • 17
    • 0033713821 scopus 로고    scopus 로고
    • Triangulations without minimum-weight drawing
    • Wang, C. A., Chin, F. Y. L., and Yang, B., Triangulations without minimum-weight drawing, Inf. Proc. Lett., 74(5–6), 183, 2000.
    • (2000) Inf. Proc. Lett , vol.74 , Issue.5-6 , pp. 183
    • Wang, C.A.1    Chin, F.Y.L.2    Yang, B.3
  • 18
    • 0033574360 scopus 로고    scopus 로고
    • Maximum weight triangulation and graph drawing
    • Wang, C. A., Chin, F. Y. L., and Yang, B. T., Maximum weight triangulation and graph drawing, Inf. Proc. Lett., 70(1), 17, 1999.
    • (1999) Inf. Proc. Lett , vol.70 , Issue.1 , pp. 17
    • Wang, C.A.1    Chin, F.Y.L.2    Yang, B.T.3
  • 19
    • 34250958061 scopus 로고
    • Uber die Zerlegung von Dreieckspolyedern in Tetraeder
    • Schönhardt, E., Uber die Zerlegung von Dreieckspolyedern in Tetraeder, Math. Annalen., 98, 309, 1928.
    • (1928) Math. Annalen , vol.98 , pp. 309
    • Schönhardt, E.1
  • 20
    • 0345655516 scopus 로고
    • On the difficulty of tetrahedralizing 3-dimensional non-convex polyhedra
    • Ruppert, J. and Seidel, R., On the difficulty of tetrahedralizing 3-dimensional non-convex polyhedra, Disc. Comput. Geom., 7, 227, 1992.
    • (1992) Disc. Comput. Geom , vol.7 , pp. 227
    • Ruppert, J.1    Seidel, R.2
  • 21
    • 85056047570 scopus 로고
    • On the difficulty of greedy tetrahedralization of points in 3D
    • Chin, F. and Wang, C. A., On the difficulty of greedy tetrahedralization of points in 3D, Proc. 7th Canadian Conf. on Comput. Geom., 1995, p. 285.
    • (1995) Proc. 7Th Canadian Conf. on Comput. Geom , pp. 285
    • Chin, F.1    Wang, C.A.2
  • 23
    • 0001516771 scopus 로고
    • Triangulating a nonconvex polytope
    • Chazelle, B. and Palios, L., Triangulating a nonconvex polytope, Disc. Comput. Geom., 5, 505, 1990.
    • (1990) Disc. Comput. Geom , vol.5 , pp. 505
    • Chazelle, B.1    Palios, L.2
  • 24
    • 1442264734 scopus 로고    scopus 로고
    • The complexity of finding small triangulations of convex 3-polytopes
    • Below, A., De Loera, J., and Richter-Gebert, J., The complexity of finding small triangulations of convex 3-polytopes, J. Algorithms, 50(2), 134, 2004.
    • (2004) J. Algorithms , vol.50 , Issue.2 , pp. 134
    • Below, A.1    De Loera, J.2    Richter-Gebert, J.3
  • 25
    • 70350637053 scopus 로고    scopus 로고
    • Optimal tetrahedralizations of some convex polyhedra
    • Wang, C. A. and Yang, B., Optimal tetrahedralizations of some convex polyhedra, EuropeanWorkshop on Comput. Geom., 2000, p. 5.
    • (2000) Europeanworkshop on Comput. Geom , pp. 5
    • Wang, C.A.1    Yang, B.2
  • 26
    • 4344568508 scopus 로고    scopus 로고
    • Minimal tetrahedralizations of a class of polyhedra
    • Yang, B. and Wang, C. A., Minimal tetrahedralizations of a class of polyhedra, J. Comb. Opt., 8(3), 241, 2004.
    • (2004) J. Comb. Opt , vol.8 , Issue.3 , pp. 241
    • Yang, B.1    Wang, C.A.2
  • 27
  • 28
    • 0003415254 scopus 로고
    • Technical Report ACT-15, Coord. Sci. Lab., University of Illinois at Urbana
    • Gilbert, P., New Results on Planar Triangulations, Technical Report ACT-15, Coord. Sci. Lab., University of Illinois at Urbana, 1979.
    • (1979) New Results on Planar Triangulations
    • Gilbert, P.1
  • 29
    • 0000775283 scopus 로고
    • Minimal triangulations of polygonal domains
    • Klincsek, G., Minimal triangulations of polygonal domains, Ann. Discrete Math., 9, 121, 1980.
    • (1980) Ann. Discrete Math , vol.9 , pp. 121
    • Klincsek, G.1
  • 30
    • 38249000218 scopus 로고
    • Polynomial time instances of the minimum weight triangulation problem
    • Anagnostou, E. and Corneil, D., Polynomial time instances of the minimum weight triangulation problem, Comput. Geom.: Theor. Appl., 3, 247, 1993.
    • (1993) Comput. Geom.: Theor. Appl , vol.3 , pp. 247
    • Anagnostou, E.1    Corneil, D.2
  • 31
    • 0040508261 scopus 로고
    • Expected case analysis of β-skeletons with applications to the construction of minimum weight triangulations
    • Cheng, S.-W., Golin, M., and Tsang, J., Expected case analysis of β-skeletons with applications to the construction of minimum weight triangulations, Proc. 7th Canadian Conf. on Comput. Geom., 1995, p. 279.
    • (1995) Proc. 7Th Canadian Conf. on Comput. Geom , pp. 279
    • Cheng, S.-W.1    Golin, M.2    Tsang, J.3
  • 34
    • 0029725197 scopus 로고    scopus 로고
    • Approaching the largest β-skeleton within a minimum weight triangulation
    • Cheng, S.-W. and Xu, Y.-F., Approaching the largest β-skeleton within a minimum weight triangulation, Proc. 12th ACM Symp. on Comput. Geom., 1996, p. 196.
    • (1996) Proc. 12Th ACM Symp. on Comput. Geom , pp. 196
    • Cheng, S.-W.1    Xu, Y.-F.2
  • 35
    • 0347140625 scopus 로고    scopus 로고
    • A lower bound for β-skeleton belonging to minimum weight triangulations, Comput
    • Wang, C. and Yang, B., A lower bound for β-skeleton belonging to minimum weight triangulations, Comput. Geom.: Theor. and Appl., 19(1), 35, 2001.
    • (2001) Geom.: Theor. and Appl , vol.19 , Issue.1 , pp. 35
    • Wang, C.1    Yang, B.2
  • 36
    • 0026845826 scopus 로고
    • Computing the minimum weight triangulation of a set of linearly ordered points
    • Meijer, H. and Rappaport, D., Computing the minimum weight triangulation of a set of linearly ordered points, Inf. Proc. Lett., 42(1), 35, 1992.
    • (1992) Inf. Proc. Lett , vol.42 , Issue.1 , pp. 35
    • Meijer, H.1    Rappaport, D.2
  • 37
    • 0347031820 scopus 로고    scopus 로고
    • Computing a minimum weight triangulation of a sparse point set
    • Wang, C. and Xu, Y., Computing a minimum weight triangulation of a sparse point set, J. Global Opt., 15, 73, 1999.
    • (1999) J. Global Opt , vol.15 , pp. 73
    • Wang, C.1    Xu, Y.2
  • 44
    • 0347870425 scopus 로고    scopus 로고
    • On exclusion regions for optimal triangulations
    • Drysdale, R. L., McElfresh, S., and Snoeyink, J., On exclusion regions for optimal triangulations, Disc. Appl. Math., 109 (1–2), 49, 2001.
    • (2001) Disc. Appl. Math , vol.109 , Issue.1-2 , pp. 49
    • Drysdale, R.L.1    McElfresh, S.2    Snoeyink, J.3
  • 45
    • 0006938345 scopus 로고
    • A note on Delaunay and optimal triangulations
    • Kirkpatrick, D. G., A note on Delaunay and optimal triangulations, Info. Proc. Lett., 10(3), 127, 1980.
    • (1980) Info. Proc. Lett , vol.10 , Issue.3 , pp. 127
    • Kirkpatrick, D.G.1
  • 46
    • 0023367455 scopus 로고
    • AnΩ(√ n) lower bound for the nonoptimality of the greedy triangulation
    • Levcopoulos, C., AnΩ(√ n) lower bound for the nonoptimality of the greedy triangulation, Inf. Proc. Lett., 25, 247, 1987.
    • (1987) Inf. Proc. Lett , vol.25 , pp. 247
    • Levcopoulos, C.1
  • 47
    • 0000024829 scopus 로고
    • A new heuristic for minimum weight triangulation
    • Lingas, A., A new heuristic for minimum weight triangulation, SIAM J. Algebraic Disc. Meth., 8(4), 646, 1987.
    • (1987) SIAM J. Algebraic Disc. Meth , vol.8 , Issue.4 , pp. 646
    • Lingas, A.1
  • 48
    • 0028713169 scopus 로고
    • New results for the minimum weight triangulation problem
    • Heath, L. and Pemmaraju, S., New results for the minimum weight triangulation problem, Algorithmica, 12(6), 533, 1994.
    • (1994) Algorithmica , vol.12 , Issue.6 , pp. 533
    • Heath, L.1    Pemmaraju, S.2
  • 49
    • 0006892634 scopus 로고    scopus 로고
    • Tight lower bounds for minimum weight triangulation heuristics
    • Levcopoulos, C. and Krznaric, D., Tight lower bounds for minimum weight triangulation heuristics, Inf. Proc. Lett., 57(3), 129, 1996.
    • (1996) Inf. Proc. Lett , vol.57 , Issue.3 , pp. 129
    • Levcopoulos, C.1    Krznaric, D.2
  • 50
    • 0006936254 scopus 로고    scopus 로고
    • Quasi-greedy triangulations approximating the minimum weight triangulation
    • Levcopoulos, C. and Krznaric, D., Quasi-greedy triangulations approximating the minimum weight triangulation, J. Algorithms, 27(2), 303, 1998.
    • (1998) J. Algorithms , vol.27 , Issue.2 , pp. 303
    • Levcopoulos, C.1    Krznaric, D.2
  • 51
    • 0000393305 scopus 로고
    • A heuristic triangulation algorithm
    • Plaisted, D. A. and Hong, J., A heuristic triangulation algorithm, J. Algorithms, 8(3), 405, 1987.
    • (1987) J. Algorithms , vol.8 , Issue.3 , pp. 405
    • Plaisted, D.A.1    Hong, J.2
  • 52
    • 52449146324 scopus 로고
    • On approximation behavior of the greedy triangulation for convex polygons
    • Levcopoulos, C. and Lingas, A., On approximation behavior of the greedy triangulation for convex polygons, Algorithmica, 2, 175, 1987.
    • (1987) Algorithmica , vol.2 , pp. 175
    • Levcopoulos, C.1    Lingas, A.2
  • 53
    • 0006890703 scopus 로고    scopus 로고
    • A linear-time approximation scheme for minimum weight triangulation of convex polygons
    • Levcopoulos, C. and Krznaric, D., A linear-time approximation scheme for minimum weight triangulation of convex polygons, Algorithmica, 21(3), 285, 1998.
    • (1998) Algorithmica , vol.21 , Issue.3 , pp. 285
    • Levcopoulos, C.1    Krznaric, D.2
  • 54
    • 0021628110 scopus 로고
    • On the average length of Delaunay triangulations
    • Chang, R. C. and Lee, R. C. T., On the average length of Delaunay triangulations, BIT, 24(3), 269, 1984.
    • (1984) BIT , vol.24 , Issue.3 , pp. 269
    • Chang, R.C.1    Lee, R.2
  • 55
    • 0346410510 scopus 로고
    • The greedy triangulation approximates the minimum weight triangulation and can be computed in linear time in the average case
    • Technical report LU-CS-TR:92-105, Department of Computer Science, Lund University, Sweden
    • Levcopoulos, C. and Lingas, A., The greedy triangulation approximates the minimum weight triangulation and can be computed in linear time in the average case, Technical report LU-CS-TR:92-105, Department of Computer Science, Lund University, Sweden, 1992. Preliminary version in Proc. ICCI ’91, Lecture Notes in Computer Science, p. 497.
    • (1992) Preliminary Version in Proc. ICCI ’91, Lecture Notes in Computer Science , pp. 497
    • Levcopoulos, C.1    Lingas, A.2
  • 56
    • 21044431562 scopus 로고    scopus 로고
    • A constant-factor approximation for maximum weight triangulation
    • Hu, S., A constant-factor approximation for maximum weight triangulation, Proc. 15th Canadian Conf. on Comput. Geom., 2003, p. 150.
    • (2003) Proc. 15Th Canadian Conf. on Comput. Geom , pp. 150
    • Hu, S.1
  • 58
    • 21044456762 scopus 로고    scopus 로고
    • A linear-time approximation scheme for maximum weight triangulation of convex polygons
    • Qian, J. and Wang, C. A., A linear-time approximation scheme for maximum weight triangulation of convex polygons, Algorithmica, 40, 161, 2004.
    • (2004) Algorithmica , vol.40 , pp. 161
    • Qian, J.1    Wang, C.A.2
  • 60
    • 0034415121 scopus 로고    scopus 로고
    • Minimal simplicial dissections and triangulations of convex 3-polytopes
    • Below, A., Brehm, U., De Loera, J. A., and Richter-Gebert, J., Minimal simplicial dissections and triangulations of convex 3-polytopes, Disc. Comput. Geom., 24(1), 35, 2000.
    • (2000) Disc. Comput. Geom , vol.24 , Issue.1 , pp. 35
    • Below, A.1    Brehm, U.2    De Loera, J.A.3    Richter-Gebert, J.4
  • 61
    • 0034413328 scopus 로고    scopus 로고
    • Finding small triangulations of polytope boundaries is hard
    • Richter-Gebert, J., Finding small triangulations of polytope boundaries is hard, Discrete Comput. Geometry, 24, 503, 2000.
    • (2000) Discrete Comput. Geometry , vol.24 , pp. 503
    • Richter-Gebert, J.1
  • 62
    • 0035630043 scopus 로고    scopus 로고
    • Approximation for minimumtriangulations of simplicial convex 3-polytopes
    • Chin, F.Y. L., Fung, S. P.Y., andWang, C. A., Approximation for minimumtriangulations of simplicial convex 3-polytopes, Disc. Comput. Geom., 26(4), 499, 2001.
    • (2001) Disc. Comput. Geom , vol.26 , Issue.4 , pp. 499
    • Chin, F.Y.L.1    Fung, S.P.Y.2    Wang, C.A.3
  • 64
    • 0022011993 scopus 로고
    • Arboricity and subgraph listing algorithms
    • Chiba, N. and Nishizeki, T., Arboricity and subgraph listing algorithms, SIAM J. Comput., 14(1), 210, 1985.
    • (1985) SIAM J. Comput , vol.14 , Issue.1 , pp. 210
    • Chiba, N.1    Nishizeki, T.2
  • 65
    • 22544484811 scopus 로고    scopus 로고
    • Approximating the minimum triangulation of convex polytopes with bounded degrees
    • Fung, S. P. Y., Chin, F. Y. L., and Poon, C. K., Approximating the minimum triangulation of convex polytopes with bounded degrees, Comput. Geom.: Theor. Appl., 32(1), 1, 2005.
    • (2005) Comput. Geom.: Theor. Appl , vol.32 , Issue.1 , pp. 1
    • Fung, S.P.Y.1    Chin, F.Y.L.2    Poon, C.K.3
  • 66
    • 0034549857 scopus 로고    scopus 로고
    • Computational geometry column 40
    • O’Rourke, J., Computational geometry column 40, Int. J. Comput. Geom. and Appl., 10(6), 649, 2000.
    • (2000) Int. J. Comput. Geom. and Appl , vol.10 , Issue.6 , pp. 649
    • O’Rourke, J.1
  • 67
    • 0032785026 scopus 로고    scopus 로고
    • Approximateminimumweight steiner triangulation in three dimensions
    • Cheng, S.-W. and Dey, T. K., Approximateminimumweight steiner triangulation in three dimensions, Proc. of SODA, 1999, p. 205.
    • (1999) Proc. of SODA , pp. 205
    • Cheng, S.-W.1    Dey, T.K.2


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